Information:
Gaussian elimination transforms a system into upper triangular form through row operations. The elimination process proceeds column by column, eliminating entries below the diagonal.
Consider the following Python code for Gaussian elimination:

def gauss_elim(A, b):
n = len(A)
for k in range(n):
for i in range(k, n):
factor = A[i][k] / A[k][k]
for j in range(k, n):
A[i][j] -= factor * A[k][j]
b[i] -= factor * b[k]
return A, b

Why does this code fail to produce the correct upper triangular matrix?

Question

Information: 
 Gaussian elimination transforms a system    into upper triangular form through row operations. The elimination process proceeds column by column, eliminating entries below the diagonal. 
Consider the following Python code for Gaussian elimination:

def gauss_elim(A, b):
    n = len(A)
    for k in range(n):
        for i in range(k, n):
            factor = A[i][k] / A[k][k]
            for j in range(k, n):
                A[i][j] -= factor * A[k][j]
            b[i] -= factor * b[k]
    return A, b

Why does this code fail to produce the correct upper triangular matrix?

Answer

The code crashes from division by zero when  A[k][k]  is zero.

Answer

The factor uses  A[k][i]  instead of  A[i][k]  for index access.

Answer

Modifying the pivot row destroys the upper triangular matrix structure.

Answer

The subtraction should be addition to eliminate below-diagonal entries.

Answer

The inner loop  j  should start from 0 to update all matrix columns.

Answer

Loop  i  starts at  k  instead of  k+1 , including the pivot row.

Crowdly

Information: Gaussian elimination transforms a system into upper triangular...

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